Download 1 ECE 305 Homework: Week 10 Mark Lundstrom

ECE 305 1)
Spring 2015 ECE 305 Homework: Week 10 Mark Lundstrom Purdue University Consider an ideal metal-­‐semiconductor junction with the band diagram shown below. The semiconductor has a relative dielectric constant of 12 and an electron affinity of 4.0 eV. Answer the following questions. 2) 1a) What is the workfunction of the metal? 1b) What is the built-­‐in potential of the semiconductor? 1c) At V = 0, we measure a capacitance of 17 pF for a 100 µm x 100 µm diode. What is the doping density in the semiconductor? You are given a metal semiconductor at room temperature in which the workfunction of the metal equals the electron affinity of the semiconductor plus 3k BT 3k T (i.e. Φ M = χ + 3k BT ) and the Fermi level in the semiconductor is 3k BT below EC . The semiconductor has a bandgap of 1 eV. 2a) Is the semiconductor n-­‐type, p-­‐type, or intrinsic? 2b) What is the numerical value of Vbi ? 2c) Is the metal contact to the semiconductor ohmic or rectifying? 3) You are given a metal semiconductor at room temperature in which the workfunction of the metal equals the electron affinity of the semiconductor plus 3k BT (i.e. Φ M = χ + 3k BT ). For this problem, the Fermi level in the semiconductor is 3k BT above EV . The semiconductor has a bandgap of 1 eV. 3a) Is the semiconductor n-­‐type, p-­‐type, or intrinsic? 3b) What is the numerical value of Vbi ? 3c) Is the metal contact to the semiconductor ohmic or rectifying? ECE-­‐305 1 Spring 2015 ECE 305 Spring 2015 HW10 (continued): 4) You are given a room temperature semiconductor with a bandap of 1.43 eV and ni = 2 × 106 cm -3 and an electron affinity of χ = 4.0 eV ideally contacted by a metal with Φ M = 4.1 eV . Answer the following questions. 4a) What is the numerical value of Φ BN ? 4b) What is the numerical value of Φ BP ? 4c) If the semiconductor is doped so that Φ M = Φ S , is the MS junction rectifying or ohmic? 4d) For the semiconductor of 4c), what is Vbi ? 5) An ideal MS diode is described by I D = I 0 eqVA
(
k BT
)
− 1 , but real diodes have series resistance. Consider an MS diode with I 0 = 10−12 A at room temperature. A forward bias of 1 V is applied and a current of 1 A is measured. What is the series resistance of this diode? ECE-­‐305 2 Spring 2015